This paper proposes a model that enables a robot to predict and imitate the motions of another by reusing its body forward-inverse model. Our model includes three approaches: (i) projection of a self-forward model for predicting phenomena in the external environment (other individuals), (ii) "triadic relation" that is mediation by a physical object between self and others, (iii) introduction of infant imitation by a parent. The Recurrent Neural Network with Parametric Bias (RNNPB) model is used as the robot's self forward-inverse model. A group of hierarchical neural networks are attached to the RNNPB model as "conversion modules". Experiments demonstrated that a robot with our model could imitate a human's motions by translating the viewpoint. It could also discriminate known/unknown motions appropriately, and associate whole motion dynamics from only one motion snap image.